Question

A wheel of a bullock cart is rolling on a level road, as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively) ?
 

• A. Point P moves slower than point Q.
• B. Point P moves faster than point Q
• C. Both the points P and Q move with equal speed.
• D. Point P has zero speed.

Answer 1

The Correct Option is B

 

Step 1: Understand Rolling Motion

In rolling motion, a point on the rim of the wheel has both rotational and translational motion. The velocities due to both these motions add vectorially.

Step 2: Analyze the Velocity at Points P and Q

Point P is at the top of the wheel. Its velocity is the sum of the linear speed (v) of the wheel and the rotational speed (v).

Point Q is at the bottom of the wheel, where the linear speed (v) and rotational speed (-v) cancel out.

Step 3: Calculate Velocities

Velocity at P:

$$ v_P = v + v = 2v $$

Velocity at Q:

$$ v_Q = v - v = 0 $$

Step 4: Conclusion

Point P moves faster than Point Q, and Point Q has zero velocity.